A275697 Primes p such that gcd(p-1, q-1) = q - p, where q is the next prime after p.

2, 3, 5, 11, 13, 17, 29, 31, 37, 41, 59, 61, 71, 73, 89, 97, 101, 107, 109, 113, 137, 149, 151, 157, 179, 181, 191, 193, 197, 227, 229, 239, 241, 269, 271, 277, 281, 311, 313, 331, 347, 349, 367, 373, 397, 401, 419, 421, 431, 433, 449, 457, 461, 521, 523

Offset

1,1

Comments

Primes prime(k) such that prime(k) == 1 (mod A001223(k)).

Problem: are there infinitely many such primes?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 1000: # to get all terms <= N
P:= select(isprime, [2, seq(i, i=3..nextprime(N), 2)]):
P[select(i -> (P[i] - 1) mod (P[i+1]-P[i]) = 0, [$1..nops(P)-1])];

Mathematica

Select[Partition[Prime[Range[100]], 2, 1], GCD[#[[1]]-1, #[[2]]-1] == #[[2]]- #[[1]]&][[All, 1]] (* Harvey P. Dale, Apr 18 2018 *)

Prog

(PARI) is(n) = ispseudoprime(n) && gcd(n-1, nextprime(n+1)-1)==nextprime(n+1)-n \\ Felix Fröhlich, Aug 06 2016

Crossrefs

Cf. A000040, A001223.

Contains A001359.

Except for 2, contained in A090190.

Sequence in context: A040044 A253110 A140549 * A127046 A127051 A127045

Adjacent sequences: A275694 A275695 A275696 * A275698 A275699 A275700

Keyword

nonn

Author

Thomas Ordowski and Robert Israel, Aug 05 2016

Status

approved